Complexity of Solving Multi-Potential Schrodinger Equation?

degerativpart
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Homework Statement


Does anyone now how to solve the schrodinger equation for a potenital such that: V1(0<x<a), v2(a<x<b), v3(b<x<c). Also i need to write down the condition which gives the possible energy eigenvalues of a particle in the potential. ITs easily to solve the first potential well but when it starts to introducing the two others I feel like I am messing up. Any help would be nice?


Homework Equations





The Attempt at a Solution


 
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You basically do what you would do in a square well, except that you match the wavefunctions at the boundaries. (I'm assuming that v1, v2 and v3 are constants.)
 
Thread 'Need help understanding this figure on energy levels'

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This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
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Thread 'Understanding how to "tack on" the time wiggle factor'

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The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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